How to take action when multiple RxJS forkjoins are complete?

You have 2 observables that you want to trigger at the same time. Simplest way is to merge them and concat with the action you want to take at the end:

const action1$ = forkjoin([item1, item2]);
const action2$ = forkjoin([item3, item4]);

concat([
  merge([action1$, action2$]),
  defer(() => {
    // this will happen after action1 and action2 are complete
    return EMPTY;
  }),
]);

You could use an outer forkJoin with iif to conditionally trigger the second observable. And pipe in finalize to perform some action on completion.

forkJoin(
  forkjoin([item1, item2]),
  iif(
    () => someCondition,
    forkjoin([item3, item4])
  )
).pipe(
  finalize(() => {
    // do something when the source observables complete
  )
)

Assuming that the second forkJoin gets triggered based on a condition depending on the result returned by the first forkJoin, I would proceed like this

forkjoin([item1, item2]).pipe(
   // use concatMap to trigger a second Observable once the firs one has emitted
   concatMap(resultOfFirst => {
      // check somehow whether the condition is met
      return isConditionMetToTriggerSecond(resultOfFirst) ? 
         forkjoin([item1, item2]).pipe(
            // use map to return both the first and the second result
            map(resultOfSecond => {
               return [resultOfFirst, resultOfSecond]
            })
         ) :
         // if the condition is not met return just the first result
         of([resultOfFirst, null])
   })
).subscribe(
   // take an action when either the first or both complete
   ([resultOfFirst, resultOfSecond]) => {
      // do something if both have been executed
      if(!!resultOfSecond) {
         // do stuff with both results
      }
   } else {  // do something if only the first has been executed
        // do stuff with first result
   }
)